The German three-times world champion, who has never won a race in Hungary, was four-tenths of a second quicker than his Australian team-mate with a benchmark time of a minute 21.264 seconds on soft tyres.
The top five drivers were covered by less than three tenths of a second.
Lotus's Romain Grosjean was the fastest of the non-Red Bull drivers ahead of the Ferraris of Fernando Alonso and Felipe Massa.
Lewis Hamilton and Mercedes team-mate Nico Rosberg were sixth and seventh respectively as Mercedes did not show the kind of one-lap pace that has secured it the last two pole positions.
Kimi Raikkonen, Jenson Button and Adrian Sutil completed the top 10 in a trouble-free session.
Vettel needed just a few minutes to move to the top of the times with the fastest lap of the weekend so far, the Red Bull driver posting a 1m22.484s 10 minutes into the running.
Although Webber managed to reduce gap as the session progressed, Vettel raised the bar at the 30-minute mark and went a full 1.2 seconds quicker with Pirelli's soft tyres.
The Australian reacted right away, however, and - also using the softs - move to within 0.044s of Vettel's time.
Rosberg's first run on softs elevated him to third place, albeit over seven tenths of a second behind the pacesetter.
Hamilton outpaced his team-mate with the yellow-marked rubber, although he too was far from Vettel's time despite Mercedes' single-lap pace.
Ferrari drivers Alonso and Massa relegated the Mercedes duo at the halfway point, with the Spaniard moving into third ahead of his Brazilian team-mate. Both men were running with the soft tyres.
Grosjean then got even closer to the Red Bulls - just 0.153s behind - and jumped to third place in the Lotus.